Deformed Conformal and Supersymmetric Quantum Mechanics

Abstract

Within the standard quantum mechanics a q-deformation of the simplest N=2 supersymmetry algebra is suggested. Resulting physical systems do not have conserved charges and degeneracies in the spectra. Instead, superpartner Hamiltonians are q-isospectral, i.e. the spectrum of one can be obtained from another by the q^2-factor scaling. A special class of the self-similar potentials is shown to obey the dynamical conformal symmetry algebra su_q(1,1). These potentials exhibit exponential spectra and corresponding raising and lowering operators satisfy the q-deformed harmonic oscillator algebra of Biedenharn and Macfarlane.

11 pages

Cited by in corpus (24)

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• Exactly Solvable Potentials and Quantum Algebras
• Harmonic oscillator with nonzero minimal uncertainties in both position and momentum in a SUSYQM framework
• More on a SUSYQM approach to the harmonic oscillator with nonzero minimal uncertainties in position and/or momentum
• Quons, coherent states and intertwining operators
• Point Canonical Transformation versus Deformed Shape Invariance for Position-Dependent Mass Schrödinger Equations
• SUSY-hierarchy of one-dimensional reflectionless potentials
• Generalized Deformed Commutation Relations with Nonzero Minimal Uncertainties in Position and/or Momentum and Applications to Quantum Mechanics
• Statistical Origin of Pseudo-Hermitian Supersymmetry and Pseudo-Hermitian Fermions
• Quantum mechanical spectral engineering by scaling intertwining
• Topological Symmetries
• Localized Fermions on Domain Walls and Extended Supersymmetric Quantum Mechanics
• Local realizations of $q$-Oscillators in Quantum Mechanics
• A nonlinear deformed su(2) algebra with a two-colour quasitriangular Hopf structure
• Two-parameter deformed supersymmetric oscillators with SUq1/q2(n|m)-covariance
• Non-isospectral Hamiltonians, intertwining operators and hidden hermiticity
• Quantum mechanics over a q-deformed (0+1)-dimensional superspace
• Central Charge Extended Supersymmetric Structures for Fundamental Fermions Around non-Abelian Vortices
• Extended Supersymmetries and 2+1 Dimensional Supersymmetric Chern Simons Theories
• Weak supersymmetry and superconformal indices